A particle of mass $m$ moves with a constant velocity $v$ parallel to the x-axis at a constant perpe

Question

A particle of mass $m$ moves with a constant velocity $v$ parallel to the x-axis at a constant perpendicular distance $d$ from it. What is the magnitude and nature of its angular momentum about the origin?

Professor PC Thomas Classes · Answer

Angular momentum is $L = r 	imes p = r 	imes (mv)$. Its magnitude is $mvr\sin	heta = mv(r\sin	heta)$. As the particle moves parallel to the x-axis, the perpendicular distance $r\sin	heta$ remains constant and is equal to $d$. Thus, magnitude is $mvd$. The direction given by the right-hand rule is perpendicular to the plane containing $r$ and $v$, which also remains constant.